Tag: entanglement

A Nightcap And Secrets

On By rolcottIn Computer science, Physics: Quantum Mechanics, UncategorizedLeave a comment

“A coffee nightcap, Sy? It’s decaf so Teena can have some.”

“Sounds good, Sis.”

“Why didn’t Mr Einstein like entanglement, Uncle Sy? Thanks, Mom. A little more cream in it, please.”

“I’ll bet it has to do with the instant-effect aspect, right, Sy?”

“Thanks, Sis, and you’re right as usual. All of Relativity theory rests on the claim that nothing, not light or gravity or causality itself, can travel faster than light in a vacuum. There’s good strong arguments and evidence to support that, but Einstein himself proved that entanglement effects aren’t constrained to lightspeed. Annoyed him no end.”

“Well, your coin story‘s very nice, but it’s just a story. Is there evidence for entanglement?”

“Oh, yes, though it was fifty years after Einstein’s entanglement paper before our technology got good enough to do the experiments. Since then a whole industry of academics and entrepreneurs has grown up to build and apply devices that generate entangled systems.”

“Systems?”

“Mm-hm. Most of the work has been done with pairs of photons, but people have entangled pairs of everything from swarms of ultra‑cold atoms to electrons trapped in small imperfect diamonds. It’s always a matter of linking the pair members through some shared binary property.”

“Binary! I know what that is. Brian has a computer toy he lets me play with. You tell it where to drive this little car and it asks for decisions like left‑right or go‑stop and they’re all yes or no and the screen shows your answer as ‘0’or ‘1’ and that’s binary, right?”

“Absolutely, Teena. The entangled thingies are always created in pairs, remember? Everything about each twin is identical except for that one property, like the two coin metals, so it’s yes, no, or some mixture. Cars can’t do mixtures because they’re too big for quantum.”

“What kinds of properties are we talking about? It’s not really gold and silver, is it?”

“No, you’re right about that, Sis. Transmutation takes way too much power. Entangled quantum states have little or no energy separation which is one reason the experiments are so hard. Photons are the easiest to work with so that’s where most of the entanglement work has been done. Typically the process splits a laser beam into two rays that have contrasting polarizations, say vertical and horizontal. Or the researchers might work with particles like electrons that you can split into right‑ and left‑handed spin. Whatever, call ’em ones and zeroes, you’ve got a bridge between quantum and computing.”

“Brian says binary can do secret codes.”

“He’s right about that. Codes are about hiding information. Entanglement is real good at hiding quantum information behind some strict rules. Rule one is, if you inspect an entangled particle, you break the entanglement.”

“Sounds reasonable. When you measure it you make it part of a big system and it’s not quantum any more.”

“Right, Sis. Rule two, an entanglement only links pairs. No triples or broadcasts. Rule three is for photons — you can have two independent ways to inspect a property, but you need to use the same way for both photons or you’ve got a 50% chance of getting a mismatch.”

“Oho! I see where the hiding comes in. Hmm… From what I’ve read, encryption’s big problem is guarding the key. I think those three rules make a good way to do that. Suppose Rocky and Bullwinkle want to protect their coded messages from Boris Badinoff. They share a series of entangled photon pairs. and they agree to a measurement protocol based on the published daily prices for a series of stocks — for each photon in a series, measure it with Method 1 if the corresponding price is an odd number, Method 2 if it’s even. Rocky measures his photon. If he measures a ‘1’ then Bullwinkle sees a ‘0’ for that photon and he knows Rocky saw a ‘1.’ Rocky encrypts his message using his measured bit string. Bullwinkle flips his bit string and decrypts.”

“Brilliant. Even if Boris knows the proper sequence of measurements, if he peeks at an entangled photon that breaks the entanglement. When Bullwinkle decodes gibberish Rocky has to build another key. Your Mom’s a very smart person, Teena.”

~ Rich Olcott

Tiramisu And Gemstones

On By rolcottIn Physics: Quantum Mechanics, UncategorizedLeave a comment

“Sis, you say there’s dessert?”

“Of course there is, Sy. Teena, please bring in the tray from the fridge.”

“Tiramisu! You did indeed go above and beyond. Thank you, Teena. Your Mom’s question must be a doozey.”

“I’ll let you enjoy a few spoonfulls before I hit you with it.” <minutes with spoon noises and yumming> “Okay. tell me about entanglement.”

“Whoa! What brought that on?”

“I’ve seen the word bandied about in the popular science press—”

“And pseudoscience—”

“Well, yes. I’m writing something where the notion might come in handy if it makes sense.”

“How can you tell what’s pseudoscience?”

“Good question, Teena. I look for gee-whiz sentences, especially ones that include weasely words like ‘might‘ and ‘could.’ Most important, does the article make or quote big claims that can’t be disproven? I’d want to see pointers to evidence strong enough to match the claims. A respectable piece would include comments from other people working in the same field. Things like that.”

“What your Mom said, and also has the author used a technical term like ‘energy‘ or ‘quantum‘ but stretched it far away from its home base? Usually when they do that and you have even an elementary idea what the term really means, it’s pretty clear that the author doesn’t understand what they’re writing about. That goes double for a lot of what you’ll see on YouTube and social media in general. It’s just so easy to put gibberish up there because there’s no‑one to contradict a claim, or if there is, it’s too late because the junk has already spread. ‘Entanglement‘ is just the latest buzzword to join the junk‑science game.”

“So what can you tell us about entanglement that’s non‑junky?”

“First thing is, it’s strictly a microscopic phenomenon, molecule‑tiny and smaller. Anything you read about people or gemstones being entangled, you can stop reading right there unless it’s for fun.”

“Weren’t Rapunzel and the prince entangled?

“They and all the movie’s other characters were tangled up in the story, yes, but that’s not the kind of entanglement your Mom’s asking about. This kind seems to involve something that Einstein called ‘spooky action at a distance‘. He didn’t like it.”

“‘Seems to‘?”

“Caught me, Sis, but it’s an important point. You make a system do something by acting on it, right? We’re used to actions where force is transmitted by direct contact, like hitting a ball with a bat. We’ve known how direct contact works with solids and fluids since Newton. We’ve extended the theory to indirect contact via electric and other fields thanks to Maxwell and Einstein and a host of other physicists. ‘Action at a distance‘ is about making something happen without either direct or indirect contact and that’s weird.”

“Can you give us an example?”

“How about an entanglement story? Suppose there’s a machine that makes coins, nicely packaged up in gift boxes. They’re for sweethearts so it always makes the coins in pairs, one gold and one silver. These are microscopic coins so quantum rules apply — every coin is half gold and half silver until its box is opened, at which point it becomes all one pure metal.”

“Like Schrödinger’s asleep‑awake kitty‑cat!”

“Exactly, Teena. So Bob buys a pair of boxes, keeps one and gives the other to Alice before he flies off in his rocket to the Moon. Quantum says both coins are both metals. When he lands, he opens his box and finds a silver coin. What kind of coin does Alice have?”

“Gold, of course.”

“For sure. Bob’s coin‑checking instantly affected Alice’s coin a quarter‑million miles away. Spooky, huh?”

“But wait a minute. Alice’s coin doesn’t move. It’s not like Bob pushed on it or anything. The only thing that changed was its composition.”

“Sis, you’ve nailed it. That’s why I said ‘seems to‘. Entanglement’s not really action at a distance. No energy or force is exerted, it’s simply an information thing about quantum properties. Which, come to think of it, is why there’s no entanglement of people or gemstones. Even a bacterium has billions and billions of quantum‑level properties. Entanglement‑tweaking one or two or even a thousand atoms won’t affect the object as a whole.”

~~ Rich Olcott

Things That Won’t Work

On By rolcottIn Physics: Light and Relativity, UncategorizedLeave a comment

Vinnie gets a far-away look in his eye. I wait. “Ya know, Sy, there oughtta be a way.”

“A way to what?”

“I ain’t giving up on this faster-than-light communication stuff. I know Einstein said it couldn’t happen because it’d flip cause and effect and he didn’t like that, but that feels too much like philosophy books I’ve read that boil down to, ‘This thing can’t be true because I don’t want it to be.’ Maybe there’s something we ain’t thought of yet.”

“Lots of people have played with that challenge for decades. Do you have any fresh ideas?”

“A couple possibles. Lessee if I’ve got this straight. We’ve got two separate message channels going — one that works instant-like for information between entangled quantum thingies, and one for everything else that’s stuck at lightspeed or less. Suppose I’ve got two entangled pizzas— nah, we’re really talking quantum stuff like electrons and photons so I’ll just say particles. Suppose I’ve got two entangled particles that are some ugly mix of red and green but we know when they’re de-linked they’ll be opposite. I send one to you the regular way but they’re still linked. I look at the one I still got and it’s red, say. The same moment, yours instantly went green but you don’t know that yet until you look or you get status information from me through the not‑instant channel. So the problem is getting information to leak between the two channels, right?”

“That’s about the size of it.”

“OK, try this one. How about I use a magnetic field or something to force mine to red? And maybe a set time later I make it green to confirm I’m in control and it’s a real signal.”

“Sorry, as soon as you manipulate properties in part of an entangled system you break the entanglement and the other part is free to do whatever it wants to. Next?”

“Uhh … time synchronization. How about you and me set a certain time for me to look at mine? You can watch yours and when it flips or not you’ll know.”

“All that does is move the manipulation to the other end of the setup. Me looking at my particle resets yours to whatever color mine isn’t and that breaks the entanglement. Next?”

“Maybe something with a bunch of particles all entangled together? How about—”

“Nup, can’t base a strategy on that. Like everything else quantum, entanglement is statistical. There’s no guarantee that even in our two‑particle system I’ll see green if you see red — the odds are high but not 100%. There’s a proven theorem that says if two particles are ‘maximally entangled,’ adding a third to the system reduces the odds that any two will coordinate their behaviors. A bunch of particles would be even less stable. It’s called the monogamy theorem, care to guess why?”

“Physics fun with metaphors again, cute, but I can see this is a good one. You got anything?”

“Not having to do with entanglement, but I have been playing with a different idea, sort of a blank‑sky approach.”

“You mean blue‑sky.”

“Uh-uh, blank. Think about a sky made of dark matter. Dark matter’s subject to gravity but so far as we know it has absolutely no interaction with electromagnetism of any kind — doesn’t play with electrons, light waves, nothing. Einstein based part of his relativity work on Maxwell’s electromagnetism equations. In fact, that’s where the idea came from that ‘c‘ was the speed limit for the Universe. It was a good idea and there’s a huge amount of evidence that he was right. Everything in our Standard Model except the photon is subject to the Lorentz factor. Both light and gravity acting on normal matter travel at c‑speed. Well, maybe the value of c has something to do with how quarks work. Dark matter doesn’t have quarks. What if dark matter has a different speed limit, maybe a lot higher than c or even no limit at all? Maybe we could exploit that property somehow. How about a dark‑matter telegraph?”

“I’m thinking of my Grampa’s recipe for rabbit stew. ‘First you gotta catch your rabbit,’ he used to say,”

~~ Rich Olcott

The Pizza Connection

On By rolcottIn Physics: Light and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

“Wait a minute, Sy. If Einstein’s logic proves we can’t have faster‑than‑light communication, what about all the entanglement hype I see in my science magazines?”

“Hype’s the right word, Vinnie. Entanglement’s a real effect, but it doesn’t play well as a communication channel.”

“OK, why not?”

“Let’s set the stage. We’re still in our personal spaceships and we’ve just ordered pizza from Eddie. The entanglement relationship is independent of time and distance so I’m going to skip over how fast we’re going and pretend that Eddie’s using transporter delivery technology, ok?”

“Fine with me,”

“Good. You order your usual double pepperoni with extra cheese, I ask for Italian sausage. Two pizza boxes suddenly appear on our respective mess tables. No reflection on Eddie, but suppose he has a history of getting orders crossed. The quantum formalism says because our orders were filled at the same time and in a single operation, the two boxes are entangled — we don’t know which is which. Before we open the boxes, each of us has a 50:50 shot of getting the right order. It’s like we’ve got a pair of Schrödinger pizzas, half one order and half the other until we look, right?”

“Won’t happen, Eddie’s a pro.”

“True, but stay with me here. I open my box and immediately I know which pizza you received, no matter how far away your ship is from mine. Is that instantaneous communication between us?”

“Of course not, I’m not gonna know which pizza either of us got until I open my own box. Then I’ll know what my meal’s gonna be and I’ll know what you’re having, too. Actually, I’m probably gonna know first because I get hungry sooner than you.”

“Good point. Anyway, entanglement doesn’t transmit human‑scale information. The only communication between us in our spaceships is still limited by Einstein’s rules. But this is a good setup for us to dig a little deeper into the quantum stuff. You rightly rejected the Schrödinger pizza idea because pizza’s human‑scale. One of those boxes definitely holds your pizza or else it definitely holds mine. There’s no in‑between mixtures with human‑scale pizzas. Suppose Eddie sent quantum‑scale nanopizzas, though. Now things get more interesting.”

“Eddie doesn’t mess up orders.”

<sigh> “Even Eddie can’t keep things straight if he sends out a pair of quantum‑scale pizzas. What’s inside a specific entangled box is called a local property. John Stewart Bell proved some statistical criteria for whether a quantum system’s properties are local or are somehow shared among the entangled objects. Scientists have applied his tests to everything from entangled photons up to little squares of diamond. They’ve tracked quantum properties from spin states to vibration modes. A lot of work went into plugging loopholes in Bell’s criteria.”

“What’d they find?”

“The results keep coming up non-local. Our quantum pizzas truly do not have separate characteristics hiding inside their boxes unless Eddie marked a box to destroy the symmetry. All the objects in an entanglement share all the applicable quantum property values until one object gets measured. Instantly, all the entangled objects snap into specific individual property values, like which box holds which pizza. They stop being entangled, too. That happens no matter how far apart they are. Those experimental results absolutely rule out the local‑property idea which was the most appealing version of the ‘underlying reality‘ that Einstein and Bohr argued over.”

“Wait, I can’t tell you anything faster than light, but these quantum thingies automatically do that instant‑like?”

“Annoying, isn’t it? But it’s a sparse form of messaging. My quantum pizza box can tell yours only two things, ‘I’ve been opened‘ and ‘I hold Italian sausage pizza.’ They’re one‑time messages at the quantum level and you as an observer can’t hear either one. Quantum theoreticians call the interaction ‘wave function collapse‘ but Einstein called it ‘spooky action at a distance.’ He hated even that limited amount of instantaneous communication because it goes directly against the first principle of Special Relativity. Relativity has been vigorously tested for over a century. It’s stood up to everything they’ve thrown at it — except for this little mouse nibbling at its base.”

~~ Rich Olcott

Schroeder’s Magic Kittycat

On By rolcottIn Physics: Quantum Mechanics, Uncategorized3 Comments

“Bedtime, Teena.”

“Aw, Mommie, I had another question for Uncle Sy.  And I’m not sleepy yet anyhow.”

“Well, if we’re just sitting here relaxing, I suppose.  Sy, make your answer as boring as possible.”

“You know me better than that, Sis, but I’ll try.  What’s your question, Teena?”

“You said something once about quantum and Schroeder’s famous kittycat.  Why is it famous?  If it’s quantum it must be a very, very small cat.  Is it magic?”

“???… Oh, Schrödinger’s Cat.  It’s a pretend cat, not a real one, but it’s famous because it’s both asleep and awake.”

“I see what you did there, Sy.”

“Yeah, Sis, but it’s for a good cause, right?”

“But Uncle Sy, how can you tell?  Sometimes Tommie our kittycat looks sound asleep but he’s not really because he can hear when Mommie opens the cat-food can.”

“Schrödinger’s Cat is special.  Whenever he’s awake his eyes are wide open and whenever he’s asleep his eyes are shut.  And he’s in a box.”

“Tommie loves to sit in boxes.”

“Schrödinger’s Cat’s box is sealed tight.  You can’t see into it.”

“So how do you know whether he’s asleep?”

“That was Mr Schrödinger’s point.  We can’t know, so we have to suppose it’s both.  Many people have made jokes about that.  Mr. Schrödinger said the usual interpretation of quantum mechanics is ridiculous and his cat story was his way of proving that.  The cat doesn’t even have to be quantum-small and the story still works.”

“How could it be halfway?  Either his eyes are open or they’re … wait, sometimes Tommie squints, is that it?”

“Nice try, but no.  Do you remember when we were looking at the bird murmuration and I asked you to point to its middle?”

“Oh, yes, and it was making a beautiful spiral.  Mommie, you should have seen it!”

“Were there any birds right at its middle?”

“Um, no-o.  All around the middle but not right there.”

“Birds to the left, birds to the right, but no birds in the middle.  But if I’d I asked you to point to the place where the birds were, you’d’ve pointed to the middle.”

“Uh-huh.”

“You see how that’s like Mr Schrödinger’s cat’s situation?  It’s really asleep or maybe it’s really awake, but if we’re asked for just one answer we’d have to say ‘halfway between.’  Which is silly just like Mr Schrödinger said — by the usual quantum calculation we’d have to consider his cat to be half awake.  That was part of the long argument between Mr Einstein and the other scientist.”

“Wait, Sy, I didn’t hear that part of you two’s conversation on the porch.  What argument was that?”

“This was Einstein’s big debate with Niels Bohr.  Bohr maintained that all we could ever know about the quantum world are the probabilities the calculations yielded.  Einstein held that the probabilities had to result from processes taking place in some underlying reality.  Cat reality here, which we can resolve by opening the box, but the same issue applies across the board at the quantum level.  The problem’s more general than it appears, because much the same issue appears any time you can have a mixture of two or more states.  Are you asleep yet, Sweetie?”

“Nnn, kp tkng.”

“OK.  Entanglement, for instance.  Pretty much the same logic that Schrödinger disparaged can also apply to quantum particles on different paths through space.  Fire off any process that emits a pair of particles, photons for instance.  The wave function that describes both of them together persists through time so if you measure a property for one of them, say polarization direction, you know what that property is for the other one without traveling to measure it.  So far, so good.  What drove Einstein to deplore the whole theory is that the first particle instantaneously notifies the other one that it’s been measured.  That goes directly counter to Einstein’s Theory of Relativity which says that communication can’t go any faster than the speed of light.  Aaand I think she’s asleep.”

“Nice job, Sy, I’ll put her to bed.  We may discuss entanglement sometime.  G’night, Sy.”

“G’night, Sis.  Let me know the next time you do that meatloaf recipe.”

Cat emerging from murmuration~~ Rich Olcott

Three Perils for a Quest(ion), Part 3

On By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

“Things are finally slowing down.  You folks got an interesting talk going, mind if I join you?  I got biscotti.”

“Pull up a chair, Eddie.  You know everybody?”

“You and Jeremy, yeah, but the young lady’s new here.”

“I’m Jennie, visiting from England.”

“Pleased to meetcha.  So from what I overheard, we got Jeremy on some kinda Quest to a black hole’s crust.  He’s passed two Perils.  There’s a final one got something to do with a Firewall.”

“One minor correction, Eddie.  He’s not going to a crust, because a black hole doesn’t have one.  Nothing to stand on or crash into, anyway.  He’s headed to its Event Horizon, which is the next best thing.  If you’re headed inward, the Horizon marks the beginning of where it’s physically impossible to get out.”

“Hotel California, eh?”

“You could say that.  The first two Perils had to do with the black hole’s intense gravitational field.  The one ahead has to do with entangled virtual particles.”

“Entangled is the Lucy-and-Ethel thing you said where two particles coordinate instant-like no matter how far apart they are?”

“Good job of overhearing, there, Eddie.  Jeremy, tell him abut virtual particles.”

“Umm, Mr Moire and I talked about a virtual particle snapping into and out of existence in empty space so quickly that the long-time zero average energy isn’t affected.”

“What we didn’t mention then is that when a virtual pair is created, they’re entangled.  Furthermore, they’re anti-particles, which means that each is the opposite of the other — opposite charge, opposite spin, opposite several other things.  Usually they don’t last long — they just meet each other again and annihilate, which is how the average energy stays at zero.  Now think about creating a pair of virtual particles in the black hole’s intense gravitational field where the creation event sends them in opposite directions.”Astronaut and semi-biscotto
“Umm… if they’re on opposite paths then one’s probably headed into the Horizon and the other is outbound. Is the outbound one Hawking radiation?  Hey, if they’re entangled that means the inbound one still has a quantum connection with the one that escaped!”

“Wait on.  If they’re entangled and something happening to one instantaneously affects its twin, but the gravity difference gives each a different rate of time dilation, how does that work then?”

“Paradox, Jennie!  That’s part of what the Firewall is about.  But it gets worse.  You’d think that inbound particle would add mass to the black hole, right?”

“Surely.”

“But it doesn’t.  In fact, it reduces the object’s mass by exactly each particle’s mass.  That ‘long-time zero average energy‘ rule comes into play here.  If the two are separated and can’t annihilate, then one must have positive energy and the other must have negative energy.  Negative energy means negative mass, because of Einstein’s mass-energy equivalence.  The positive-mass twin escapes as Hawking radiation while the negative-mass twin joins the black hole, shrinks it, and by the way, increases its temperature.”

“Surely not, Sy.  Temperature is average kinetic energy.  Adding negative energy to something has to decrease its temperature.”

“Unless the something is a black hole, Jennie.  Hawking showed that a black hole’s temperature is inversely dependent on its mass.  Reduce the mass, raise the temperature, which is why a very small black hole radiates more intensely than a big one.  Chalk up another paradox.”

“Two paradoxes.  Negative mass makes no sense.  I can’t make a pizza with negative cheese.  People would laugh.”

“Right.  Here’s another.  Suppose you drop some highly-structured object, say a diamond, into a black hole.  Sooner or later, much later really, that diamond’s mass-energy will be radiated back out.  But there’s no relationship between the structure that went in and the randomized particles that come out.  Information loss, which is totally forbidden by thermodynamics.  Another paradox.”

“The Firewall resolves all these paradoxes then?”

“Not really, Jennie.  The notion is that there’s this thin layer of insanely intense energetic interactions, the Firewall, just outside of the Event Horizon.  That energy is supposed to break everything apart — entanglements, pre-existing structures, quantum propagators (don’t ask), everything, so what gets through the horizon is mush.  Many physicists think that’s bogus and a cop-out.”

“So no Firewall Peril?”

“Wanna take the chance?”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 2

On By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

Eddie came over to our table.  “Either you folks order something else or I’ll have to charge you rent.”  Typical Eddie.

“Banana splits sound good to you two?”

[Jeremy and Jennie] “Sure.”

“OK, Eddie, two banana splits, plus a coffee, black, for me.  And an almond biscotti.”

“You want one, that’s a biscotto.”

“OK, a biscotto, Eddie.  The desserts are on my tab.”

“Thanks, Mr Moire.”

“Thanks, Sy.  I know you want to get on to the third Peril on Jeremy’s Quest for black hole evaporation, but how does he get past the Photon Sphere?”

“Yeah, how?”

“Frankly, Jeremy, the only way I can think of is to accept a little risk and go through it really fast.  At 2/3 lightspeed, for instance, you and your two-meter-tall suit would transit that zero-thickness boundary in about 10 nanoseconds.  In such a short time your atoms won’t get much out of position before the electromagnetic fields that hold your molecules together kick back in again.”

“OK, I’ve passed through.  On to the Firewall … but what is it?”

“An object of contention, for one thing.  A lot of physicists don’t believe it exists, but some claim there’s evidence for it in the 2015 LIGO observations.  It was proposed a few years ago as a way out of some paradoxes.”

“Ooo, Paradoxes — loverly.  What’re the paradoxes then?”

“Collisions between some of the fundamental principles of Physics-As-We-Know-It.  One goes back to the Greeks — the idea that the same thing can’t be in two places at once.”

“Tell me about it.  Here’s your desserts.”

“Thanks, Eddie.  The place keeping you busy, eh?”

“Oh, yeah.  Gotta be in the kitchen, gotta be runnin’ tables, all the time.”

“I could do wait-staff, Mr G.  I’m thinking of dropping track anyway, Mr Moire, 5K’s don’t have much in common with base running which is what I care about.  How about I show up for work on Monday, Mr G?”

“Kid calls me ‘Mr’ — already I like him.  You’re on, Jeremy.”

“Woo-hoo!  So what’s the link between the Firewall and the Greeks?”

“Link is the right word, though the technical term is entanglement.  If you create two particles in a single event they seem to be linked together in a way that really bothered Einstein.”

“For example?”Astronaut and biscotti
“Polarizing sunglasses.  They depend on a light wave’s crosswise electric field running either up-and-down or side-to-side.  Light bouncing off water or road surface is predominately side-to-side polarized, so sunglasses are designed to block that kind.  Imagine doing an experiment that creates a pair of photons named Lucy and Ethel.  Because of how the experiment is set up, the two must have complementary polarizations.  You confront Lucy with a side-to-side filter.  That photon gets through, therefore Ethel should be blocked by a side-to-side filter but should go through an up-and-down filter.  That’s what happens, no surprise.  But suppose your test let Lucy pass an up-and-down filter.  Ethel would pass a side-to-side filter.”

“But Sy, isn’t that because each photon has a specific polarization?”

“Yeah, Jennie, but here’s the weird part — they don’t.  Suppose you confront Lucy with a filter set at some random angle.  There’s only the one photon, no half-way passing, so either it passes or it doesn’t.  Whenever Lucy chooses to pass, Ethel usually passes a filter perpendicular to that one.  It’s like Ethel hears from Lucy what the deal was — and with zero delay, no matter how far away the second test is executed.  It’s as though Lucy and Ethel are a single particle that occupies two different locations.  In fact, that’s exactly how quantum mechanics models the situation.  Quite contrary to the Greeks’ thinking.”

“You said that Einstein didn’t like entanglement, either.  How come?”

“Einstein published the original entanglement mathematics in the 30s as a counterexample against Bohr’s quantum mechanics.  The root of his relativity theories is that the speed of light is a universal speed limit.  If nothing can go faster than light, instantaneous effects like this can’t happen.  Unfortunately, recent experiments proved him wrong.  Somehow, both Relativity and Quantum Mechanics are right, even though they seem to be incompatible.”

“And this collision is why there’s a problem with black hole evaporation?”

“It’s one of the collisions.”

“There’s more?  Loverly.”

~~ Rich Olcott

Reflections in Einstein’s bubble

On By rolcottIn Mathematics: Dimensions, Physics: Black Holes and Relativity, Physics: Light and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

There’s something peculiar in this earlier post where I embroidered on Einstein’s gambit in his epic battle with Bohr.  Here, I’ll self-plagiarize it for you…

Consider some nebula a million light-years away.  A million years ago an electron wobbled in the nebular cloud, generating a spherical electromagnetic wave that expanded at light-speed throughout the Universe.

Last night you got a glimpse of the nebula when that lightwave encountered a retinal cell in your eye.  Instantly, all of the wave’s energy, acting as a photon, energized a single electron in your retina.  That particular lightwave ceased to be active elsewhere in your eye or anywhere else on that million-light-year spherical shell.

Suppose that photon was yellow light, smack in the middle of the optical spectrum.  Its wavelength, about 580nm, says that the single far-away electron gave its spherical wave about 2.1eV (3.4×10-19 joules) of energy.  By the time it hit your eye that energy was spread over an area of a trillion square lightyears.  Your retinal cell’s cross-section is about 3 square micrometers so the cell can intercept only a teeny fraction of the wavefront.  Multiplying the wave’s energy by that fraction, I calculated that the cell should be able to collect only 10-75 joules.  You’d get that amount of energy from a 100W yellow light bulb that flashed for 10-73 seconds.  Like you’d notice.

But that microminiscule blink isn’t what you saw.  You saw one full photon-worth of yellow light, all 2.1eV of it, with no dilution by expansion.  Water waves sure don’t work that way, thank Heavens, or we’d be tsunami’d several times a day by earthquakes occurring near some ocean somewhere.

Feynman diagramHere we have a Feynman diagram, named for the Nobel-winning (1965) physicist who invented it and much else.  The diagram plots out the transaction we just discussed.  Not a conventional x-y plot, it shows Space, Time and particles.  To the left, that far-away electron emits a photon signified by the yellow wiggly line.  The photon has momentum so the electron must recoil away from it.

The photon proceeds on its million-lightyear journey across the diagram.  When it encounters that electron in your eye, the photon is immediately and completely converted to electron energy and momentum.

Here’s the thing.  This megayear Feynman diagram and the numbers behind it are identical to what you’d draw for the same kind of yellow-light electron-photon-electron interaction but across just a one-millimeter gap.

It’s an essential part of the quantum formalism — the amount of energy in a given transition is independent of the mechanical details (what the electrons were doing when the photon was emitted/absorbed, the photon’s route and trip time, which other atoms are in either neighborhood, etc.).  All that matters is the system’s starting and ending states.  (In fact, some complicated but legitimate Feynman diagrams let intermediate particles travel faster than lightspeed if they disappear before the process completes.  Hint.)

Because they don’t share a common history our nebular and retinal electrons are not entangled by the usual definition.  Nonetheless, like entanglement this transaction has Action-At-A-Distance stickers all over it.  First, and this was Einstein’s objection, the entire wave function disappears from everywhere in the Universe the instant its energy is delivered to a specific location.  Second, the Feynman calculation describes a time-independent, distance-independent connection between two permanently isolated particles.  Kinda romantic, maybe, but it’d be a boring movie plot.

As Einstein maintained, quantum mechanics is inherently non-local.  In QM change at one location is instantaneously reflected in change elsewhere as if two remote thingies are parts of one thingy whose left hand always knows what its right hand is doing.

Bohr didn’t care but Einstein did because relativity theory is based on geometry which is all about location. In relativity, change here can influence what happens there only by way of light or gravitational waves that travel at lightspeed.

In his book Spooky Action At A Distance, George Musser describes several non-quantum examples of non-locality.  In each case, there’s no signal transmission but somehow there’s a remote status change anyway.  We don’t (yet) know a good mechanism for making that happen.

It all suggests two speed limits, one for light and matter and the other for Einstein’s “deeper reality” beneath quantum mechanics.

~~ Rich Olcott

Gin And The Art of Quantum Mechanics

On By rolcottIn Physics: Quantum Mechanics, Uncategorized2 Comments

“Fancy a card game, Johnny?”
“Sure, Jennie, deal me in.  Wot’re we playin’?”
“Gin rummy sound good?”

Great idea, and it fits right in with our current Entanglement theme.  The aspect of Entanglement that so bothered Einstein, “spooky action at a distance,” can be just as spooky close-up.  Check out this magic example — go ahead, it’s a fun trick to figure out.

Spooky, hey?  And it all has to do with cards being two-dimensional.  I know, as objects they’ve got three dimensions same as anyone (four, if you count time), but functionally they have only two dimensions — rank and suit.gin rummy hand

When you’re looking at a gin rummy hand you need to consider each dimension separately.  The queens in this hand form a set — three cards of the same rank.  So do the three nines.  In the suit dimension, the 4-5-6-7 run is a sequence of ranks all in the same suit.Gin rummy chart

A physicist might say that evaluating a gin rummy hand is a separable problem, because you can consider each dimension on its own. <Hmm … three queens, that’s a set, and three nines, another set.  The rest are hearts.  Hey, the hearts are in sequence, woo-hoo!> 

“Gin!”

If you chart the hand, the run and sets and their separated dimensions show up clearly even if you don’t know cards.

A standard strategy for working a complex physics problem is to look for a way to split one kind of motion out from what else is going on.  If the whole shebang is moving in the z-direction, you can address  the z-positions, z-velocities and z-forces as an isolated sub-problem and treat the x and y stuff separately.  Then, if everything is rotating in the xy plane you may be able to separate the angular motion from the in-and-out (radial) motion.

But sometimes things don’t break out so readily.  One nasty example would be several massive stars flying toward each other at odd angles as they all dive into a black hole.  Each of the stars is moving in the black hole’s weirdly twisted space, but it’s also tugged at by every other star.  An astrophysicist would call the problem non-separable and probably try simulating it in a computer instead of setting up a series of ugly calculus problems.Trick chart

The card trick video uses a little sleight-of-eye to fake a non-separable situation.  Here’s the chart, with green dots for the original set of cards and purple dots for the final hand after “I’ve removed the card you thought of.”  The kings are different, and so are the queens and jacks.  As you see, the reason the trick works is that the performer removed all the cards from the original hand.

The goal of the illusion is to confuse you by muddling ranks with suits.  What had been a king of diamonds in the first position became a king of spades, whereas the other king became a queen.  You were left with an entangled perception of each card’s two dimensions.

In quantum mechanics that kind of entanglement crops up any time you’ve got two particles with a common history.  It’s built into the math — the two particles evolve together and the model gives you no way to tell which is which.

Suppose for instance that an electron pair has zero net spin  (spin direction is a dimension in QM like suit is a dimension in cards).  If the electron going to the left is spinning clockwise, the other one must be spinning counterclockwise.  Or the clockwise one may be the one going to the right — we just can’t tell from the math which is which until we test one of them.  The single test settles the matter for both.

Einstein didn’t like that ambiguity.  His intuition told him that QM’s statistics only summarize deeper happenings.  Bohr opposed that idea, holding that QM tells us all we can know about a system and that it’s nonsense to even speak of properties that cannot be measured.  Einstein called the deeper phenomena “elements of reality” though they’re currently referred to as “hidden variables.”  Bohr won the battle but maybe not the war — Einstein had such good intuition.

~~ Rich Olcott

Oh, what an entangled wave we weave

On By rolcottIn Physics: Quantum Mechanics, UncategorizedLeave a comment

“Here’s the poly bag wiff our meals, Johnny.  ‘S got two boxes innit, but no labels which is which.”
“I ordered the mutton pasty, Jennie, anna fish’n’chips for you.”
“You c’n have this box, Johnny.  I’ll take the other one t’ my place to watch telly.”
…
<ring>
” ‘Ullo, Jennie?  This is Johnny.  The box over ‘ere ‘as the fish.  You’ve got mine!”

In a sense their supper order arrived in an entangled state.  Our friends knew what was in both boxes together, but they didn’t know what was in either box separately.  Kind of a Schrödinger’s Cat situation — they had to treat each box as 50% baked pasty and 50% fried codfish.

But as soon as Johnny opened one box, he knew what was in the other one even though it was somewhere else.  Jennie could have been in the next room or the next town or the next planet — Johnnie would have known, instantly, which box had his meal no matter how far away that other box was.

By the way, Jennie was free to open her box on the way home but that’d make no difference to Johnnie — the box at his place would have stayed a mystery to him until either he opened it or he talked to her.

Entangled 2Information transfer at infinite speed?  Of course not, because neither hungry person knows what’s in either box until they open one or until they exchange information.  Even Skype operates at light-speed (or slower).

But that’s not quite quantum entanglement, because there’s definite content (meat pie or batter-fried cod) in each box.  In the quantum world, neither box holds something definite until at least one box is opened.  At that point, ambiguity flees from both boxes in an act of global correlation.

There’s strong experimental evidence that entangled particles literally don’t know which way is up until one of them is observed.  The paired particle instantaneously gets that message no matter how far away it is.

Niels Bohr’s Principle of Complementarity is involved here.  He held that because it’s impossible to measure both wave and particle properties at the same time, a quantized entity acts as a wave globally and only becomes local when it stops somewhere.

Here’s how extreme the wave/particle global/local thing can get.  Consider some nebula a million light-years away.  A million years ago an electron wobbled in the nebular cloud, generating a spherical electromagnetic wave that expanded at light-speed throughout the Universe.

cats-eye nebula
The Cat’s Eye Nebula (NGC 6543)
courtesy of NASA’s Hubble Space Telescope

Last night you got a glimpse of the nebula when that lightwave encountered a retinal cell in your eye.  Instantly, all of the wave’s energy, acting as a photon, energized a single electron in your retina.  That particular lightwave ceased to be active elsewhere in your eye or anywhere else on that million-light-year spherical shell.

Surely there was at least one other being, on Earth or somewhere else, that was looking towards the nebula when that wave passed by.  They wouldn’t have seen your photon nor could you have seen any of theirs.  Somehow your wave’s entire spherical shell, all 1012 square lightyears of it, instantaneously “knew” that your eye’s electron had extracted the wave’s energy.

But that directly contradicts a bedrock of Einstein’s Special Theory of Relativity.  His fundamental assumption was that nothing (energy, matter or information) can go faster than the speed of light in vacuum.  STR says it’s impossible for two distant points on that spherical wave to communicate in the way that quantum theory demands they must.

Want some irony?  Back in 1906, Einstein himself “invented” the photon in one of his four “Annus mirabilis” papers.  (The word “photon” didn’t come into use for another decade, but Einstein demonstrated the need for it.)  Building on Planck’s work, Einstein showed that light must be emitted and absorbed as quantized packets of energy.

It must have taken a lot of courage to write that paper, because Maxwell’s wave theory of light had been firmly established for forty years prior and there’s a lot of evidence for it.  Bottom line, though, is that Einstein is responsible for both sides of the wave/particle global/local puzzle that has bedeviled Physics for a century.

~~ Rich Olcott